Lesson 6 Let’s Investigate Solidify Understanding

Ready

Solve each system of equations.

1.

${\begin{cases} 2 x + 3 y = 9 \\ - 2 x - 5 y = 1 \end{cases}$

2.

${\begin{cases} 3 x + 2 y = 5 \\ 4 x - 5 y = 22 \end{cases}$

3.

${\begin{cases} 5 x - 2 y = 20 \\ 7 x + 4 y = 11 \end{cases}$

4.

${\begin{cases} 2 x - 4 y = 5 \\ - x + 2 y = 8 \end{cases}$

5.

${\begin{cases} 5 x - 7 y = - 16 \\ x + 4 y = 13 \end{cases}$

6.

${\begin{cases} - 3 + 2 y = 4 \\ 9 x - 6 y = - 12 \end{cases}$

7.

Write ${\begin{cases} 3 x + 2 y = 5 \\ 4 x - 5 y = 22 \end{cases}$ as an augmented matrix.

8.

Write ${\begin{cases} x + y + z = 1 \\ x + 3 y + 7 z = 13 \\ x + 2 y + 3 z = 4 \end{cases}$ as an augmented matrix.

Set

For the following scenarios, identify each situation as a survey, observational study, or an experiment.

9.

To determine if a new pain medication is effective, researchers randomly assign two groups of people to use the pain medication in group 1 and a placebo in group 2. Both groups are asked to rate their pain and the results are compared.

A.

survey

B.

observational study

C.

experiment

10.

Officials want to determine if raising the speed limit from $75 mph$ to $80 mph$ will have an impact on safety. To determine this, they watch a stretch of the highway when the speed limit is $75$ and see how many accidents there are. They then observe the number of accidents over a period of time on the same stretch of highway for a speed limit of $80 mph$ and compare the difference.

A.

survey

B.

observational study

C.

experiment

11.

To determine if a new sandwich on the menu is preferred more than the original, the manager of the restaurant takes a random sample of customers who have tried both sandwiches and asks them which sandwich they like best.

A.

survey

B.

observational study

C.

experiment

12.

A newspaper wants to know how satisfied their customers are. It randomly selects $500 customers$ and asks them.

A.

survey

B.

observational study

C.

experiment

Mrs. Williams wants to know if doing practice problems actually helps students do better on their unit exams.

13.

Describe how Mrs. Williams could carry out a survey to determine if practice helps. Explain the role of randomization in your design.

14.

Describe how Mrs. Williams could carry out an observational study to determine if practice problems help test scores.

15.

Describe how Mrs. Williams could carry out an experiment to determine if practice problems help test scores. Explain how you will use randomization in your design and how you will use a control.

16.

If Mrs. Williams wants to determine if practice problems cause test scores to rise, which method would be best? Why?

Go

17.

The average resting heart rate of a young adult is approximately $70 beats$ per minute with a standard deviation of $10 beats$ per minute. Assuming resting heart rate follows a normal distribution, answer the following questions.

Draw and label the normal curve that describes this distribution. Be sure to label the mean, and the measurements $1$ , $2$ , and $3$ standard deviations out from the mean.
What percent of people have a heart rate between $55$ and $80 beats$ per minute? Label these points on your normal curve above and shade in the area that represents the percent of people with heartbeats between $55$ and $80 beats$ per minute.

18.

If a resting heart rate above $80 beats$ per minute is considered unhealthy, what percent of people have an unhealthy heart rate?